The number 10024
10024 is a composite number with 16 divisors. Its prime factorisation is × 7 × 179. Divisors (16): 1, 2, 4, 7, 8, 14, 28, 56, 179, 358, 716, 1253, 1432, 2506, 5012, 10024.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 10024: a Harshad number: divisible by its digit sum 7.
- 2
10024 is composite. Its prime factorisation is
- 3
The divisors add up to 21600; without 10024 itself that is 11576, so 10024 is abundant (11576 is more than 10024). Euler's totient φ(10024) = 4272 numbers up to 10024 share no factor with it.
- 4
The digits of 10024 add up to 7, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 135 steps to reach 1.
LaTeX source of the formulas on this page
\[ 10024 = 2^{3} \times 7 \times 179 \]10024 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 16 |
| Sum of divisors | 21600 |
| Euler totient φ(n) | 4272 |
| Square | 100480576 |
| Cube | 1007217293824 |
| Square root | 100.119928 (= 2√2506) |
| Digit sum / digital root | 7 / 7 |
| Collatz steps to 1 | 135 |
| Scientific notation | 1.0024 × |
10024 in other forms
| Form | Value |
|---|---|
| In words | ten thousand and twenty-four |
| Binary (base 2) | 10011100101000 |
| Octal (base 8) | 23450 |
| Hexadecimal (base 16) | 2728 |
| Base 3 | 111202021 |
| As time | 10024 seconds = 2 h 47 min 4 s |
Is 10024 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (10024 ÷ 2 = 5012) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (10024 ÷ 4 = 2506) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 4) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | Yes (10024 ÷ 7 = 1432) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (10024 ÷ 8 = 1253) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 4) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 4) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 10024 a prime number?
No. 10024 = × 7 × 179, so it is divisible by 2.
What are the factors of 10024?
1, 2, 4, 7, 8, 14, 28, 56, 179, 358, 716, 1253, 1432, 2506, 5012, 10024.
What is 10024 in binary?
10011100101000 (hexadecimal 2728, octal 23450).
What is the square root of 10024?
About 100.1199, exactly 2√2506.
Is 10024 divisible by 3?
No. Its digits add up to 7, which is not a multiple of 3.
What is special about the number 10024?
10024 is a Harshad number: divisible by its digit sum 7.